Two-dimensional Numerical Simulation Of Thermocapillary Convection In Detached Solidification

Detached Bridgman technique, combining appealing characteristics of both the classical Bridgman and Czochralski methods, can provide a low temperature gradient and an environment of crystal freely growth in the process of crystal solidification. It is a good method for the crystal growth and can yield high quality and bulk mass crystals of CdZnTe which is a good semi-conducting material of using widely. It can instruct experiment of growing crystal on the earth of studying the fundamental characteristics of detached solidification of the CdZnTe. So our research is significant and valuable.In this paper, the two-dimensional physical model and governing equations for CdZnTe in detached solidification are established. Numerical simulations of flow in the melt with different conditions are conducted using the finite-difference method. As a result, the distribution profiles of temperature and stream function of the melt and the critical Marangoni numbers are obtained. As well as the fundamental characteristics of flow and the physical mechanism of the unstable convection are analyzed.The results showed that: (1) When the top surface of the melt is solid wall under microgravity condition, the thermocapillary convection is caused in the melt by the surface tension gradient on the free surface. As the Marangoni number is small, the flow is steady thermocapillary convection; With the Marangoni number exceeds the critical value, the steady flow converts into unstable thermocapillary convection. The critical Marangoni number climbs with the ratio of height and radius decreasing and the gap width increasing. The physical mechanism of the unstable thermocapillary convection can be explained as a hysteretic phenomenon between the variety of velocity and temperature which caused by a velocity turbulence. (2) When the top surface of the melt is free surface under microgravity, two roll cells with opposite direction are observed in the melt, which are driven by both the surface tension gradient on the upper and lower free surfaces; Comparing the results of this part with that obtained under condition of solid wall of the top surface, it can be found that the critical Marangoni number decreases as the ratio of height and radius equals to 1 and increase as it equals to 2. (3) When the top surface of the melt is free surface under gravity condition, the effect of the buoyancy on the flow is little as the Marangoni number is small; With the Marangoni number increasing, the effect of the buoyancy increases, which makes the upper roll cell weaken and the lower roll cell strengthen; In addition, the critical Marangoni number decreases by one order of magnitude as a results of effect of buoyancy.